Related papers: Direct Domain Decomposition Method (D3M) for Finit…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We present an analysis of fermionic dark matter (DM) in the context of 6 dimensional Effective Field Theory (EFT). We also compared the result generated via the 6-dimensional EFT analysis with the current experimental results for dark…
We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional…
Standard approaches to domain decomposition methods (DDM) are uncapable of producing block-diagonal system matrices. The derived-vector-space (DVS), approach to DDM, introduced in 2013, overcomes this limitation. However, the DVS approach…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear,…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…
This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems with heterogeneous coefficients. The local approximation…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based…